the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

Expansion of (x+y)n upto 3 term
‚ÄčnC0xn+nC1xn-1y+nC2xn-2y2+......
So we are given
nC0 xn=1xn=1 ......................... (i) 
and

nC1xn-1y=56nxn-1y=56nxnyx=56nyx=56 .......................................(ii)
nC2xn-2y2=1372n(n-1)xny22x2=1372n(n-1)y22x2=1372n(n-1)2562n2=1372  from 2nd equation 1568(n-1)=1372n1568n-1372n=1568196n=1568n=8
From equation (i) we have
xn=1x8=1x=1
From equation(ii) we have
nyx=568y=56y=7
So x=1, y =7, n=8

  • 50

x = 1 , y = 7

n = 8

Very long proof.

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